Related papers: Discrete averaging relations for micro to macro tr…
Numerical simulations and a mean-field analysis of a sandpile model of earthquake aftershocks in 1d, 2d and 3d euclidean lattices determine that the average stress decays in a punctuated fashion after a main shock, with events occurring at…
We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…
Discrete element (DEM) simulations demonstrate that granular materials are non-simple, meaning that the incremental stiffness of a granular assembly depends on the gradients of the strain increment as well as on the strain increment itself.…
The fundamental interactions between an edge dislocation and a random solid solution are studied by analyzing dislocation line roughness profiles obtained from molecular dynamics simulations of Fe0.70Ni0.11 Cr0.19 over a range of stresses…
This paper introduces a stabilized finite element scheme for the Cahn--Hilliard cross-diffusion model, which is characterized by strongly coupled mobilities, nonlinear diffusion, and complex cross-diffusion terms. These features pose…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The…
Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for such materials. The so-called relaxed micromorphic model…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
Yielding transition in isotropic soft materials under superposition of orthogonal deformation fields is known to follow von Mises criterion. However, in anisotropic soft materials von Mises criterion fails owing to preferred directions…
This paper presents a hybrid continuum discrete macro modelling strategy with a multiscale calibration procedure for realistic simulations of brick masonry bridges. The response of these structures is affected by the intrinsic nonlinearity…
In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
Metal rolling is a widespread and well-studied process, and many finite-element (FE) rolling simulations can be found in the scientific literature. However, these FE simulations are typically limited in their resolution of through-thickness…
In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…